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Semi-global analysis of periodic and quasi-periodic k:1 and k:2 resonances

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  • Wagener, F.O.O.

    (Universiteit van Amsterdam)

Abstract

The present paper investigates a family of nonlinear oscillators at Hopf bifurcation, driven by a small quasi-periodic forcing. In particular, we are interested in the situation that at bifurcation and for vanishing forcing strength, the driving frequency and the normal frequency are in k:1 or k:2 resonance. For small but nonvanishing forcing strength, a semi-global normal form system is found by averaging and applying a van der Pol transformation. The bifurcation diagram is organised by a codimension 3 singularity of nilpotent-elliptic type. A fairly complete analysis of local bifurcations is given; moreover, all the nonlocal bifurcation curves predicted by Dumortier et al. (1991) are found numerically.

Suggested Citation

  • Wagener, F.O.O., 2006. "Semi-global analysis of periodic and quasi-periodic k:1 and k:2 resonances," CeNDEF Working Papers 06-06, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    • Handle: RePEc:ams:ndfwpp:06-06
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